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Rewriting Logic as a Semantic Framework for Concurrency: a Progress Report
, 1996
"... . This paper surveys the work of many researchers on rewriting logic since it was first introduced in 1990. The main emphasis is on the use of rewriting logic as a semantic framework for concurrency. The goal in this regard is to express as faithfully as possible a very wide range of concurrency mod ..."
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Cited by 82 (22 self)
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. This paper surveys the work of many researchers on rewriting logic since it was first introduced in 1990. The main emphasis is on the use of rewriting logic as a semantic framework for concurrency. The goal in this regard is to express as faithfully as possible a very wide range of concurrency models, each on its own terms, avoiding any encodings or translations. Bringing very different models under a common semantic framework makes easier to understand what different models have in common and how they differ, to find deep connections between them, and to reason across their different formalisms. It becomes also much easier to achieve in a rigorous way the integration and interoperation of different models and languages whose combination offers attractive advantages. The logic and model theory of rewriting logic are also summarized, a number of current research directions are surveyed, and some concluding remarks about future directions are made. Table of Contents 1 In...
Research Directions in Rewriting Logic
, 1998
"... Rewriting logic expresses an essential equivalence between logic and computation. System states are in bijective correspondence with formulas, and concurrent computations are in bijective correspondence with proofs. Given this equivalence between computation and logic, a rewriting logic axiom of the ..."
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Cited by 31 (12 self)
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Rewriting logic expresses an essential equivalence between logic and computation. System states are in bijective correspondence with formulas, and concurrent computations are in bijective correspondence with proofs. Given this equivalence between computation and logic, a rewriting logic axiom of the form t \Gamma! t 0 has two readings. Computationally, it means that a fragment of a system 's state that is an instance of the pattern t can change to the corresponding instance of t 0 concurrently with any other state changes; logically, it just means that we can derive the formula t 0 from the formula t. Rewriting logic is entirely neutral about the structure and properties of the formulas/states t. They are entirely userdefinable as an algebraic data type satisfying certain equational axioms. Because of this ecumenical neutrality, rewriting logic has, from a logical viewpoint, good properties as a logical framework, in which many other logics can be naturally represented. And, computationally, it has also good properties as a semantic framework, in which many different system styles and models of concurrent computation and many different languages can be naturally expressed without any distorting encodings. The goal of this paper is to provide a relatively gentle introduction to rewriting logic, and to paint in broad strokes the main research directions that, since its introduction in 1990, have been pursued by a growing number of researchers in Europe, the US, and Japan. Key theoretical developments, as well as the main current applications of rewriting logic as a logical and semantic framework, and the work on formal reasoning to prove properties of specifications are surveyed.
An Actor Rewriting Theory
, 1996
"... We present a semantic framework for actor systems based on rewriting logic. This framework accounts for fairness and provides a variety of semantics for actor system components that have good composability properties. 1 Introduction We are interested in developing a semantic foundation for open dis ..."
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Cited by 27 (8 self)
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We present a semantic framework for actor systems based on rewriting logic. This framework accounts for fairness and provides a variety of semantics for actor system components that have good composability properties. 1 Introduction We are interested in developing a semantic foundation for open distributed systems that supports specifying, composing, and reasoning about components of open distributed systems. We take the actor model of computation [12,1,2] as our starting point. Actors are independent computational agents that interact solely via message passing. An actor can create other actors; send messages; and modify its own local state. An actor can only effect the local state of other actors by sending them messages, and it can only send messages to its acquaintances  addresses of actors it was given upon creation, it received in a message or actors it created. Actor semantics requires computations to be fair. We take two views of actors: as individuals and as elements of com...
ZeroSafe Nets, or Transition Synchronization Made Simple
 PROC. OF EXPRESS’97
, 1997
"... In addition to ordinary places, called stable, zerosafe nets are equipped with zero places, which in a stable marking cannot contain any token. An evolution between two stable markings, instead, can be a complex computation called stable transaction, which may use zero places, but which is atomic w ..."
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Cited by 17 (13 self)
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In addition to ordinary places, called stable, zerosafe nets are equipped with zero places, which in a stable marking cannot contain any token. An evolution between two stable markings, instead, can be a complex computation called stable transaction, which may use zero places, but which is atomic when seen from stable places: no stable token generated in a transaction can be reused in the same transaction. Every zerosafe net has an ordinary PlaceTransition net as its abstract counterpart, where only stable places are maintained, and where every transaction becomes a transition. The two nets allow us to look at the same system from both an abstract and a refined viewpoint. To achieve this result no new interaction mechanism is used, besides the ordinary tokenpushing rules of nets. The refined zerosafe nets can be much smaller than their corresponding abstract P/T nets, since they take advantage of a transition synchronization mechanism. For instance, when transactions of unlimited l...
Concatenable graph processes: relating processes and derivation traces
 IN PROCEEDINGS OF ICALP’98, VOLUME 1443 OF LNCS
, 1998
"... Several formal concurrent semantics have been proposed for graph rewriting, a powerful formalism for the specification of concurrent and distributed systems which generalizes P/T Petri nets. In this paper we relate two such semantics recently proposed for the algebraic doublepushout approach to gra ..."
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Cited by 17 (13 self)
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Several formal concurrent semantics have been proposed for graph rewriting, a powerful formalism for the specification of concurrent and distributed systems which generalizes P/T Petri nets. In this paper we relate two such semantics recently proposed for the algebraic doublepushout approach to graph rewriting, namely the derivation trace and the graph process semantics. The notion of concatenable graph process is
Transactions and ZeroSafe Nets
 Advances in Petri Nets: Unifying Petri Nets, Lect. Notes in Comput. Sci. 2128
, 2001
"... When employing Petri nets to model distributed systems, one must be aware that the basic activities of each component can vary in duration and can involve smaller internal activities, i.e., that transitions are conceptually refined into transactions. We present an approach to the modeling of transac ..."
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Cited by 15 (8 self)
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When employing Petri nets to model distributed systems, one must be aware that the basic activities of each component can vary in duration and can involve smaller internal activities, i.e., that transitions are conceptually refined into transactions. We present an approach to the modeling of transactions based on zerosafe nets. They extend ordinary pt nets with a simple mechanism for transition synchronization. We show that the net theory developed under the two most diffused semantic interpretations (collective token and individual token philosophies) can be uniformly adapted to zerosafe nets. In particular, we show that each zerosafe net has associated two pt nets which represent the abstract counterparts of the modeled system according to the two philosophies. We show several applications of the framework, a distributed interpreter for zs nets based on classical net unfolding (here extended with a commit rule) and discuss some extensions to other net flavours.
Axioms for Contextual Net Processes
 In Automata, Languages and Programming, volume 1443 of LNCS
, 1998
"... . In the classical theory of Petri nets, a process is an operational description of the behaviour of a net, which takes into account the causal links between transitions in a sequence of firing steps. In the categorical framework developed in [19, 11], processes of a P/T net are modeled as arrows of ..."
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Cited by 14 (9 self)
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. In the classical theory of Petri nets, a process is an operational description of the behaviour of a net, which takes into account the causal links between transitions in a sequence of firing steps. In the categorical framework developed in [19, 11], processes of a P/T net are modeled as arrows of a suitable monoidal category: In this paper we lay the basis of a similar characterization for contextual P/T nets, that is, P/T nets extended with read arcs, which allows a transition to check for the presence of a token in a place, without consuming it. 1 Introduction Petri nets [24] are probably the best studied and most used model for concurrent systems: Their range of applications covers a wide spectrum, from their use as a specification tool to their analysis as a suitable semantical domain. A recent extension to the classical model concerns a class of nets where transitions are able to check for the presence of a token in a place without actually consuming it. While the possibility ...
A comparison of Petri net semantics under the collective token philosophy
 SpringerVerlag LNCS
, 1998
"... Abstract. In recent years, several semantics for place/transition Petri nets have been proposed that adopt the collective token philosophy. We investigate distinctions and similarities between three such models, namely configuration structures, concurrent transition systems, and (strictly) symmetric ..."
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Cited by 14 (9 self)
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Abstract. In recent years, several semantics for place/transition Petri nets have been proposed that adopt the collective token philosophy. We investigate distinctions and similarities between three such models, namely configuration structures, concurrent transition systems, and (strictly) symmetric (strict) monoidal categories. Weusethenotionof adjunction to express each connection. We also present a purely logical description of the collective token interpretation of net behaviours in terms of theories and theory morphisms in partial membership equational logic.
Normal Forms for Partitions and Relations
 Recent Trends in Algebraic Development Techniques, volume 1589 of Lect. Notes in Comp. Science
, 1999
"... Recently there has been a growing interest towards algebraic structures that are able to express formalisms different from the standard, treelike presentation of terms. Many of these approaches reveal a specific interest towards their application in the "distributed and concurrent systems" field, b ..."
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Cited by 14 (11 self)
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Recently there has been a growing interest towards algebraic structures that are able to express formalisms different from the standard, treelike presentation of terms. Many of these approaches reveal a specific interest towards their application in the "distributed and concurrent systems" field, but an exhaustive comparison between them is difficult because their presentations can be quite dissimilar. This work is a first step towards a unified view, which is able to recast all those formalisms into a more general one, where they can be easily compared. We introduce a general schema for describing a characteristic normal form for many algebraic formalisms, and show that those normal forms can be thought of as arrows of suitable concrete monoidal categories.